dorsal/arxiv
View SchemaResonances of Multichannel Systems
| Authors | Alexander K. Motovilov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0702178 |
| URL | https://arxiv.org/abs/quant-ph/0702178 |
| Journal | Models and Methods in Few- and Many-Body Systems. Proc. of the DST-UNISA-JINR Symposium/Ed.: S.A.Sofianos (UNISA Press, Pretoria 2007), pp. 136--150 |
Abstract
We describe structure of the T-matrices, scattering matrices, and Green functions on unphysical energy sheets in multichannel scattering problems with binary channels and in the three-body problem. Based on the explicit representations obtained for the values of T- and S-matrices on the unphysical sheets, we prove that the resonances belonging to an unphysical sheet are just those energies where the correspondingly truncated scattering matrix, taken in the physical sheet, has eigenvalue zero. We show, in addition, that eigenvectors of the truncated scattering matrix associated with its zero eigenvalue are formed of the breakup amplitudes for the respective resonant states.
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"abstract": "We describe structure of the T-matrices, scattering matrices, and Green\nfunctions on unphysical energy sheets in multichannel scattering problems with\nbinary channels and in the three-body problem. Based on the explicit\nrepresentations obtained for the values of T- and S-matrices on the unphysical\nsheets, we prove that the resonances belonging to an unphysical sheet are just\nthose energies where the correspondingly truncated scattering matrix, taken in\nthe physical sheet, has eigenvalue zero. We show, in addition, that\neigenvectors of the truncated scattering matrix associated with its zero\neigenvalue are formed of the breakup amplitudes for the respective resonant\nstates.",
"arxiv_id": "quant-ph/0702178",
"authors": [
"Alexander K. Motovilov"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"nucl-th"
],
"journal_ref": "Models and Methods in Few- and Many-Body Systems. Proc. of the\n DST-UNISA-JINR Symposium/Ed.: S.A.Sofianos (UNISA Press, Pretoria 2007), pp.\n 136--150",
"title": "Resonances of Multichannel Systems",
"url": "https://arxiv.org/abs/quant-ph/0702178"
},
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